Solve for $x$ : $6x^2 - 12x - 378 = 0$
Answer: Dividing both sides by $6$ gives: $ x^2 {-2}x {-63} = 0 $ The coefficient on the $x$ term is $-2$ and the constant term is $-63$ , so we need to find two numbers that add up to $-2$ and multiply to $-63$ The two numbers $7$ and $-9$ satisfy both conditions: $ {7} + {-9} = {-2} $ $ {7} \times {-9} = {-63} $ $(x + {7}) (x {-9}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 7) (x -9) = 0$ $x + 7 = 0$ or $x - 9 = 0$ Thus, $x = -7$ and $x = 9$ are the solutions.